Geodesic
On operators generating conditional bases in a Hilbert space
Matematičeskie zametki, Tome 12 (1972) no. 1, pp. 73-84.

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A spectral characterization is given to the linear operators which in a Hilbert space transform some complete orthonormal system into a conditional basis. 
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     author = {A. M. Olevskii},
     title = {On operators generating conditional bases in a {Hilbert} space},
     journal = {Matemati\v{c}eskie zametki},
     pages = {73--84},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_1_a9/}
}
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A. M. Olevskii. On operators generating conditional bases in a Hilbert space. Matematičeskie zametki, Tome 12 (1972) no. 1, pp. 73-84. http://geodesic.mathdoc.fr/item/MZM_1972_12_1_a9/